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The Search For The 'Body' Of The Neutrino
An anonymous reader writes: "CNN has an interesting story about the scientists who are searching for proof that neutrinos have mass a half mile below Minnesota. Not alot of scientific theory but a good overall perspective on what is taking place. One of the more interesting quotes: "We're going to take a sawed-off shotgun and blast a bunch of neutrinos toward Minnesota and measure what sticks," said Marvin Marshak, a physics professor at the University of Minnesota."
You're right that even massless things are deflected by curved spacetime, so it's a bad definition of mass. Neutrino mass is just like the mass of an electron -- or the mass of a brick. You can think of it as the resistance to acceleration by an outside force. The difference is that neutrino masses are inferred without seeing the neutrino accelerate. The process in question is neutrino oscillation; basically, the neutrino changes flavors from, say, a muon neutrino to a tau neutrino. This oscillation phenomenon comes from a weird mismatch between how the neutrino behaves under different conditions -- and one of those conditions requires mass. So seeing neutrino oscillations implies that neutrinos have mass.